Cover the damaged area of the table top with a clean dry towel.
Iron over the towel with the iron on a medium setting, no steam. Keep the iron pressed down over the stain for 30 seconds.
Lift towel to check results. The warmth of the iron should be sufficient to draw and evaporate the moisture back out of the table.
Repeat the ironing process until the area is dry, the ring has faded and dampness ceases to enter the towel. This may take several applications totaling two to three minutes, but the entire ring should come out.
If the area of the ring still appears lighter than the rest of the table, try rubbing it with a broken walnut or Brazil nut kernel--the oils in nuts help darken the wood. Blend this into the rest of the finish for a uniform look.
Rub the entire table with lemon oil or polish with your usual furniture cleaner.
For stubborn rings, it may be necessary to buff the ring out with fine-grade wire wool. Iron first to ensure wood is dry before sanding. After sanding, rub with the nut to enhance color. Polish.